Abstract

The primary aim is to unify the definition of solution for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems like, for example, a semilinear evolution equation (of parabolic type) in combination with a first order geometric evolution. In regard to geometric evolutions, this concept is to fulfill 3 conditions : First, consider nonempty compact subsets K(t) of R^N without a priori restrictions on the regularity of the boundary. Second, the evolution of K(t) might depend on nonlocal properties of the set K(t) and its normal cones. Last, but not least, no inclusion principle. The approach here is based on generalizing the mutational equations of Aubin for metric spaces in two respects : Replacing the metric by a countable family of (possibly nonsymmetric) distances (called ostensible metrics) and extending the basic idea of distributions.